Can I win with holding both Battlefields on my opponent's turn?

No, you cannot win the game by holding battlefields during your opponent's turn.

According to the game rules, scoring points through Holding occurs specifically during your own Beginning Phase.

• Holding: You score points for holding a battlefield at the start of your turn (during your Beginning Phase).
• Conquering: You score points for conquering a battlefield during your own turn (Action Phase).

Because the "Hold" scoring mechanic is tied to the start of your own turn, you cannot trigger a win condition by holding battlefields while it is your opponent's turn.